Our current research on metal-organic frameworks (MOFs) focuses primarily on their physical properties, including their remarkable mechanical, optical, magnetic, ferroelectric and electronic behaviour. We have worked extensively on the amorphization of MOFs, which can be induced thermally, under pressure, or by milling [1]. In certain cases we have been able to form glassy MOFs by quenching of the molten state [2]. I shall discuss several cases of phase transitions that depend heavily on framework flexibility. These include the transition from a porous to a dense framework at 160K in the Zeolitic Imidazolate Framework, ZIF-4, which is accompanied by a decrease in volume of ~23% [3]. A second example involves a reversible, pressure-induced phase transition in a dense rare-earth formate, which shows the breaking and making of bonds during a transition that is accompanied by a 10% change in volume [4]. In addition, we shall explore chemical transformations that depend on flexibility. These include the topochemical dehalogenation of a copper trithiocyanurate framework that is accompanied by a change from an insulating crystalline phase to an amorphous semiconductor [5], an insulator to proton conductor transition that is driven by hydration [6], and an in situ study of the successive crystallization of MOFs with increasing stability [7]. Finally, a brief summary of some of our recent work on hybrid perovskites will also be presented [8].